Question

can someone please explain implicit differentiation and how it differs to "normal" differentiation

Answer 1

It's not all too different. Its a process that helps with equations that can't be expressed explicitly with one variable completely isolated on one side. So when you differentiate something like 2y^2 with respect to x, the process is nearly identical except you need to multiply by dy/dx because of the chain rule. So think of it this way: d/dx 2(y(x))^2. You then have 4(y(x)) times the derivative of the inner function y(x) which is dy/dx. From here on you proceed to group the terms with a dy/dx on one side, factor out the dy/dx and solve for it. This is sometimes a lot easier than solving for y, THEN differentiating explicitly.